Frequently Asked Questions

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7. Computing with GAP

7.7: How do I get the subgroups of my group?

Everything said for elements holds even more so for subgroups: You probably want only representatives of the conjugacy classes or even just of subgroups of a given size.

For groups of moderate size (up to 10⁴/10⁵, this depends a bit on the group structure) the commands LatticeSubgroups or ConjugacyClassesSubgroups will compute representatives of all subgroups up to conjugacy. If the group gets bigger, however, this will either run out of space or take too long to be feasible.

In this case it is likely that you are only interested in certain types of subgroups. Try to use the restricting conditions to reduce the calculation (for example p-subgroups can be found inside a Sylow subgroup). GAP commands that might come useful to obtain specific subgroups are for example NormalSubgroups, SylowSubgroup, HallSubgroup, or MaximalSubgroupClassReps.